Module PHYS2631: THEORETICAL PHYSICS 2

Department: Physics

PHYS2631: THEORETICAL PHYSICS 2

Prerequisites

• Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus and Probability I (MATH1061) and Linear Algebra I (MATH1071))).

Corequisites

• Foundations of Physics 2A (PHYS2581).

Excluded Combination of Modules

• Mathematical Physics II (MATH2071).

Aims

• This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.
• It provides a working knowledge of classical mechanics and complements the quantum mechanics content of the module Foundations of Physics 2A by providing theoretical rigour.

Content

• The syllabus contains:
• Classical Mechanics: Lagrangian mechanics; Variational calculus and its application; Linear oscillators; One-dimensional systems and central forces; Noetherʼs theorem and Hamiltonian mechanics; Theoretical mechanics; Rotating coordinate systems; Dynamics of rigid bodies; Theory of small vibrations.
• Quantum Theory: State of a system and Dirac notation; Linear operators, eigenvalues, Hermitean operators; Expansion of eigenfunctions; Commutation relations, Heisenberg uncertainty; Unitary transforms; Matrix representations; Schrödinger equation and time evolution; Schrödinger, Heisenberg and Interaction pictures; Symmetry principles and conservation; Angular momentum (operator form); Orbital angular momentum (operator form); General angular momentum (operator form); Matrix representation of angular momentum operators; Spin angular momentum; Spin ½; Pauli spin matrices; Total angular momentum; Addition of angular momentum.

Learning Outcomes

• Having studied this module students will have developed an appreciation of the Lagrangian and Hamiltonian formulations of classical mechanics and be able to describe the rotational motion of a rigid body.
• They will be able to describe elements of quantum mechanics in a rigorous mathematical way and to manipulate them at the operator level.

• In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems.
• They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Teaching will be by lectures and tutorial-style workshops.
• The lectures provide the means to give a concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of the written material, or by information and relevant links on DUO.
• Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.
• Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.
• Student performance will be summatively assessed through an examination and formatively assessed through problem exercises and progress tests. The examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress tests and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Problem exercises and self-assessment; two progress tests, workshops (not compulsory) and problems solved therein.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University